Problem

Part 5 of 5 $z_{\alpha / 2}$ for the $94 \%$ confidence interval \[ z_{\alpha / 2}=\square \quad 5 \]

Solution

Step 1 :The problem is asking for the z-score for a 94% confidence interval. The z-score is a measure of how many standard deviations an element is from the mean. In the context of confidence intervals, the z-score tells us how far we need to go from the mean to capture the central 94% of the data.

Step 2 :To find the z-score for a 94% confidence interval, we need to find the z-score such that the area under the standard normal curve between -z and z is 0.94. This leaves 0.06 of the area outside the interval, split equally on both sides, so each tail has an area of 0.03.

Step 3 :We can use a standard normal distribution table or a calculator to find the z-score corresponding to an area of 0.97 (0.94 + 0.03) to the left of the z-score.

Step 4 :By doing so, we find that the z-score is approximately 1.88.

Step 5 :Final Answer: The \(z_{\alpha / 2}\) for the 94% confidence interval is approximately \(\boxed{1.88}\).

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Source: https://solvelyapp.com/problems/BzgGmBJlc6/

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